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arXiv · 2009.02061

A Note on the Phase Retrieval of Holomorphic Functions

Rolando Perez Iii
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Abstract

We prove that if f and g are holomorphic functions on an open connected domain, with the same moduli on two intersecting segments, then f = g up to the multiplication of a unimodular constant, provided the segments make an angle that is an irrational multiple of $\pi$. We also prove that if f and g are functions in the Nevanlinna class, and if |f | = |g| on the unit circle and on a circle inside the unit disc, then f = g up to the multiplication of a unimodular constant.

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Rolando Perez Iii. 2020-09-04. A Note on the Phase Retrieval of Holomorphic Functions. https://doi.org/10.4153/s000843952000082x

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